Why do some papers have 10-20 co-authors?

In my field, where author numbers between one and six are the norm, reasons for having more include the following:

• The paper results from a large-scale collaboration between different groups that developed different parts of the overall work.
• The paper is supposed to give a broad picture overview of something, like in the case of a survey paper or a research roadmap paper. The authors are experts for the different considered areas.
• The paper results from a collaborative brainstorming effort. Such papers are sometimes written by the participants of a research meeting (like the famous Dagstuhl seminars), or a breakout group from such.
• The paper results from a student project, and most of the co-authors are actually students.

De facto, co-authorship means different things in different fields.

As Zenon mention in their answer, the Higgs Boson paper has 5154 authors. Does that mean that there is a first author who sent around the manuscript to all co-authors, then waited for 5153 people to give feedback and OK? No, absence of response does not hold up publication and is taken as agreement on the content. As I understand it, on this collaboration, the criterion for co-authorship were that you'd been part of the team for a year (source: personal communication).

In my field (Earth Observation), there are sometimes papers on validations or campaigns that include many different instruments. For each instrument there is a PI and their postdoc and/or PhD student, who should be on the paper even if their only contribution is "provide data". They need that to prove to their funding agencies that the data are being used for science. With 10 instruments, that can easily mean 20–30 or more co-authors.

So to answer your question: it depends. The reasons for papers to have many co-authors are field and even sub-field dependent.

See also: Academia varies more than you think it does – The Movie

There are many reasons. Science is becoming more and more collaborative, especially in fields requiring experiments. See for example the ATLAS and CMS paper on the discovery of the Higgs Boson which has 5,154 authors, or this 1000 Genome project paper which has hundreds.

Those are extreme examples, but with the increase in complexity it is often required to recruit collaborators with a large amount of complementary skills to be able to gather the data and analyze it.

There are also discussions about what really warrants authorship and how those rules are not necessarily clear. There is an interesting discussion on the blog of PLOS about that.